Uniqueness on recovery of Lamé constants by the same boundary measurement

Abstract

Abstract We consider the recovery of Lamé constants and an unknown inner core in elastic system. In this paper, we use layer potential technique to represent the solution of the equation and analyze the obtained solution using transmission conditions across the boundary. Firstly, in a single-layer structure, using the same boundary measurements, we utilize the obtained solution to uniquely recover the Lamé constant. Then, in a two-layer structure, we also prove a Calderón-type identity and use this identity to uniquely recover the piecewise Lamé constant through the same boundary measurements. Finally, we prove that in a two-layer structure, the unique recovery of piecewise Lamé constant in the quasi-static regime.